12n
0175
(K12n
0175
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 11 4 6 5 8 9 10
Solving Sequence
3,8 4,10
11 7 6 9 12 1 5 2
c
3
c
10
c
7
c
6
c
8
c
11
c
12
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.04267 × 10
26
u
13
− 2.24065 × 10
27
u
12
+ ··· + 1.09231 × 10
29
b + 2.46093 × 10
28
,
− 1.28732 × 10
26
u
13
− 2.92904 × 10
27
u
12
+ ··· + 2.18462 × 10
29
a − 1.14504 × 10
29
,
u
14
+ 21u
13
+ ··· + 544u + 256i
I
u
2
= h−102u
8
− 440u
7
− 440u
6
− 655u
5
+ u
4
− 240u
3
+ 269u
2
+ 59b − 180u + 261,
− 15u
8
− 30u
7
+ 88u
6
+ 72u
5
+ 283u
4
+ 107u
3
+ 253u
2
+ 59a + 36u + 172,
u
9
+ 5u
8
+ 8u
7
+ 13u
6
+ 10u
5
+ 11u
4
+ 5u
3
+ 6u
2
+ u + 1i
I
u
3
= h−2u
5
a + 10u
4
a − 2u
5
− 30u
3
a + 13u
4
+ 33u
2
a − 45u
3
− 14au + 78u
2
+ 6b + 4a − 62u + 28,
18u
5
a + 39u
5
+ ··· + 16a − 220, u
6
− 7u
5
+ 26u
4
− 51u
3
+ 52u
2
− 28u + 8i
I
u
4
= h2u
2
b + b
2
− bu + 4u
2
+ 4b − 2u + 7, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
I
v
1
= ha, −v
3
− 7v
2
+ 4b − 12v −1, v
4
+ 7v
3
+ 16v
2
+ 13v + 4i
I
v
2
= ha, −v
2
b + b
2
+ 2bv −v
2
+ b + 2v + 1, v
3
− 3v
2
+ 2v −1i
* 6 irreducible components of dim
C
= 0, with total 51 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.04 × 10
26
u
13
− 2.24 × 10
27
u
12
+ · · · + 1.09 × 10
29
b + 2.46 ×
10
28
, −1.29 × 10
26
u
13
− 2.93 × 10
27
u
12
+ · · · + 2.18 × 10
29
a − 1.15 ×
10
29
, u
14
+ 21u
13
+ · · · + 544u + 256i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
0.000589262u
13
+ 0.0134075u
12
+ ··· − 0.805195u + 0.524136
0.000954555u
13
+ 0.0205129u
12
+ ··· + 0.318887u − 0.225296
a
11
=
0.000589262u
13
+ 0.0134075u
12
+ ··· − 0.805195u + 0.524136
0.000671621u
13
+ 0.0148039u
12
+ ··· − 0.393936u − 0.489753
a
7
=
u
u
3
+ u
a
6
=
0.00121747u
13
+ 0.0251618u
12
+ ··· + 2.10350u + 0.0491900
0.000115085u
13
+ 0.00299760u
12
+ ··· + 0.828767u − 0.0553136
a
9
=
0.00122256u
13
+ 0.0260104u
12
+ ··· + 0.0388506u + 0.499449
0.000709347u
13
+ 0.0153553u
12
+ ··· + 0.361561u − 0.145546
a
12
=
0.000261393u
13
+ 0.00718595u
12
+ ··· − 1.58109u + 0.503456
0.00106954u
13
+ 0.0235741u
12
+ ··· − 0.362940u − 0.280603
a
1
=
0.000424271u
13
+ 0.00989082u
12
+ ··· − 0.674232u + 0.474041
0.0000149496u
13
+ 0.00111721u
12
+ ··· − 0.559577u − 0.359209
a
5
=
−0.000409321u
13
− 0.00877361u
12
+ ··· + 0.114654u − 0.833250
0.0000359381u
13
+ 0.00108264u
12
+ ··· − 0.358027u − 0.313673
a
2
=
0.000409321u
13
+ 0.00877361u
12
+ ··· − 0.114654u + 0.833250
0.0000149496u
13
+ 0.00111721u
12
+ ··· − 0.559577u − 0.359209
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00674689u
13
− 0.136707u
12
+ ··· − 11.6248u − 11.8608
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 54u
13
+ ··· − 7647u + 256
c
2
, c
4
u
14
− 16u
13
+ ··· + 31u − 16
c
3
, c
7
u
14
+ 21u
13
+ ··· + 544u + 256
c
5
, c
8
u
14
+ 2u
13
+ ··· + 4u + 1
c
6
, c
9
u
14
− 11u
13
+ ··· + 9u − 9
c
10
, c
12
u
14
+ 27u
13
+ ··· + 157u − 1
c
11
u
14
+ 22u
13
+ ··· + 88u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 910y
13
+ ··· − 40412737y + 65536
c
2
, c
4
y
14
− 54y
13
+ ··· + 7647y + 256
c
3
, c
7
y
14
− 177y
13
+ ··· − 226304y + 65536
c
5
, c
8
y
14
− 2y
13
+ ··· − 6y + 1
c
6
, c
9
y
14
− 61y
13
+ ··· − 927y + 81
c
10
, c
12
y
14
− 413y
13
+ ··· − 22155y + 1
c
11
y
14
− 64y
13
+ ··· − 2456y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.126413 + 1.064170I
a = 0.0178207 − 0.1327570I
b = 0.073229 + 0.409880I
2.38888 + 2.31349I 1.040974 + 0.185703I
u = −0.126413 − 1.064170I
a = 0.0178207 + 0.1327570I
b = 0.073229 − 0.409880I
2.38888 − 2.31349I 1.040974 − 0.185703I
u = 0.594510 + 0.411375I
a = −0.944868 + 0.799301I
b = −0.88821 + 1.42199I
−3.64308 + 0.88750I −15.9778 + 0.0604I
u = 0.594510 − 0.411375I
a = −0.944868 − 0.799301I
b = −0.88821 − 1.42199I
−3.64308 − 0.88750I −15.9778 − 0.0604I
u = 1.40610 + 0.22467I
a = 0.307958 + 1.309810I
b = 0.030088 + 0.287966I
0.10775 − 7.50729I −7.28452 + 4.95143I
u = 1.40610 − 0.22467I
a = 0.307958 − 1.309810I
b = 0.030088 − 0.287966I
0.10775 + 7.50729I −7.28452 − 4.95143I
u = −0.560428
a = −0.0120122
b = −0.522964
−1.12206 −9.20330
u = −0.345517 + 0.363205I
a = 1.121570 + 0.274743I
b = −0.330774 + 0.391733I
−0.921235 + 1.059300I −5.51258 − 4.57245I
u = −0.345517 − 0.363205I
a = 1.121570 − 0.274743I
b = −0.330774 − 0.391733I
−0.921235 − 1.059300I −5.51258 + 4.57245I
u = −1.80958 + 2.11291I
a = −1.248730 − 0.134703I
b = −2.16984 + 0.05278I
19.0076 + 14.9612I −6.21836 − 5.88234I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.80958 − 2.11291I
a = −1.248730 + 0.134703I
b = −2.16984 − 0.05278I
19.0076 − 14.9612I −6.21836 + 5.88234I
u = −3.79852 + 1.13400I
a = 1.41552 + 0.05510I
b = 2.07852 + 0.02544I
−18.1348 − 0.1387I −2.93027 + 5.79154I
u = −3.79852 − 1.13400I
a = 1.41552 − 0.05510I
b = 2.07852 − 0.02544I
−18.1348 + 0.1387I −2.93027 − 5.79154I
u = −12.2807
a = 1.54847
b = 2.18693
−17.8723 0
6
II. I
u
2
= h−102u
8
− 440u
7
+ · · · + 59b + 261, −15u
8
− 30u
7
+ · · · + 59a +
172, u
9
+ 5u
8
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
0.254237u
8
+ 0.508475u
7
+ ··· − 0.610169u − 2.91525
1.72881u
8
+ 7.45763u
7
+ ··· + 3.05085u − 4.42373
a
11
=
0.254237u
8
+ 0.508475u
7
+ ··· − 0.610169u − 2.91525
2.01695u
8
+ 9.03390u
7
+ ··· + 3.55932u − 3.66102
a
7
=
u
u
3
+ u
a
6
=
−1.08475u
8
− 6.16949u
7
+ ··· − 4.79661u − 2.69492
−0.593220u
8
− 4.18644u
7
+ ··· − 3.57627u − 4.86441
a
9
=
0.491525u
8
+ 1.98305u
7
+ ··· + 1.22034u − 2.16949
2.38983u
8
+ 10.7797u
7
+ ··· + 5.86441u − 3.20339
a
12
=
−1.23729u
8
− 6.47458u
7
+ ··· − 7.83051u − 1.74576
−2.74576u
8
− 14.4915u
7
+ ··· − 13.6102u − 4.91525
a
1
=
0.491525u
8
+ 1.98305u
7
+ ··· − 0.779661u − 1.16949
0.0677966u
8
+ 0.135593u
7
+ ··· − 0.762712u − 1.64407
a
5
=
0.423729u
8
+ 1.84746u
7
+ ··· − 0.0169492u + 0.474576
−0.254237u
8
− 0.508475u
7
+ ··· + 0.610169u + 1.91525
a
2
=
0.423729u
8
+ 1.84746u
7
+ ··· − 0.0169492u + 0.474576
0.0677966u
8
+ 0.135593u
7
+ ··· − 0.762712u − 1.64407
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
142
59
u
8
+
756
59
u
7
+
1287
59
u
6
+
1997
59
u
5
+
2096
59
u
4
+
1528
59
u
3
+
1554
59
u
2
+
792
59
u +
480
59
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 10u
8
+ 29u
7
− 39u
6
+ 26u
5
− 15u
4
+ 19u
3
− 8u
2
− 3u − 1
c
2
u
9
+ 4u
8
+ 3u
7
− 5u
6
− 10u
5
− 5u
4
+ 3u
3
+ 6u
2
+ 3u + 1
c
3
u
9
+ 5u
8
+ 8u
7
+ 13u
6
+ 10u
5
+ 11u
4
+ 5u
3
+ 6u
2
+ u + 1
c
4
u
9
− 4u
8
+ 3u
7
+ 5u
6
− 10u
5
+ 5u
4
+ 3u
3
− 6u
2
+ 3u − 1
c
5
, c
8
u
9
− 3u
8
+ 5u
7
− 4u
6
+ 2u
5
− 2u
4
+ 4u
3
− 3u
2
+ 1
c
6
, c
9
u
9
− 3u
7
+ 4u
6
− 2u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1
c
7
u
9
− 5u
8
+ 8u
7
− 13u
6
+ 10u
5
− 11u
4
+ 5u
3
− 6u
2
+ u − 1
c
10
, c
12
u
9
+ 6u
8
+ 5u
7
+ 12u
6
+ 6u
5
+ 10u
4
+ 5u
2
− u + 1
c
11
u
9
− 3u
8
− 7u
7
+ 61u
6
− 171u
5
+ 279u
4
− 297u
3
+ 212u
2
− 97u + 23
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 42y
8
+ ··· − 7y −1
c
2
, c
4
y
9
− 10y
8
+ 29y
7
− 39y
6
+ 26y
5
− 15y
4
+ 19y
3
− 8y
2
− 3y −1
c
3
, c
7
y
9
− 9y
8
− 46y
7
− 109y
6
− 164y
5
− 171y
4
− 113y
3
− 48y
2
− 11y −1
c
5
, c
8
y
9
+ y
8
+ 5y
7
+ 10y
5
− 6y
4
+ 12y
3
− 5y
2
+ 6y −1
c
6
, c
9
y
9
− 6y
8
+ 5y
7
− 12y
6
+ 6y
5
− 10y
4
− 5y
2
− y −1
c
10
, c
12
y
9
− 26y
8
+ ··· − 9y −1
c
11
y
9
− 23y
8
+ ··· − 343y −529
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699225 + 0.881171I
a = 0.153901 − 0.439956I
b = −0.480829 − 0.332872I
−1.28188 + 7.91801I −11.0500 − 9.5481I
u = −0.699225 − 0.881171I
a = 0.153901 + 0.439956I
b = −0.480829 + 0.332872I
−1.28188 − 7.91801I −11.0500 + 9.5481I
u = −0.293070 + 1.131440I
a = −0.518996 + 0.755920I
b = −0.365565 − 0.116422I
1.91580 − 3.10870I −3.25080 + 5.79361I
u = −0.293070 − 1.131440I
a = −0.518996 − 0.755920I
b = −0.365565 + 0.116422I
1.91580 + 3.10870I −3.25080 − 5.79361I
u = 0.355075 + 0.694524I
a = −0.776460 − 0.463249I
b = 0.258201 − 0.760917I
1.44595 − 4.09337I −1.10458 + 4.89395I
u = 0.355075 − 0.694524I
a = −0.776460 + 0.463249I
b = 0.258201 + 0.760917I
1.44595 + 4.09337I −1.10458 − 4.89395I
u = −0.046807 + 0.509508I
a = −2.11030 − 0.01768I
b = −3.48539 + 1.47690I
−1.03199 − 3.67986I 3.16209 + 3.89016I
u = −0.046807 − 0.509508I
a = −2.11030 + 0.01768I
b = −3.48539 − 1.47690I
−1.03199 + 3.67986I 3.16209 − 3.89016I
u = −3.63195
a = 1.50371
b = 2.14716
−18.5451 −22.5130
10
III. I
u
3
= h−2u
5
a − 2u
5
+ · · · + 4a + 28, 18u
5
a + 39u
5
+ · · · + 16a −
220, u
6
− 7u
5
+ 26u
4
− 51u
3
+ 52u
2
− 28u + 8i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
a
1
3
u
5
a +
1
3
u
5
+ ··· −
2
3
a −
14
3
a
11
=
a
1
3
u
5
a +
1
3
u
5
+ ··· −
2
3
a −
14
3
a
7
=
u
u
3
+ u
a
6
=
1
12
u
5
a −
1
3
u
5
+ ··· − 3a +
17
6
1
2
u
5
a −
17
12
u
5
+ ··· −
10
3
a + 3
a
9
=
1
6
u
5
a +
1
12
u
5
+ ··· +
2
3
a −
5
2
7
6
u
5
a +
7
12
u
5
+ ··· −
14
3
a −
19
3
a
12
=
−
1
8
u
5
+
7
8
u
4
+ ··· −
13
2
u +
7
2
1
6
u
5
a −
19
12
u
5
+ ··· −
8
3
a +
20
3
a
1
=
19
24
u
5
−
35
8
u
4
+ ··· +
35
3
u − 3
2
3
u
5
−
11
3
u
4
+ ··· +
32
3
u −
11
3
a
5
=
−
1
8
u
5
+
17
24
u
4
+ ··· − u −
2
3
1
2
u
5
−
17
6
u
4
+ ··· + 7u −
7
3
a
2
=
1
8
u
5
−
17
24
u
4
+ ··· + u +
2
3
2
3
u
5
−
11
3
u
4
+ ··· +
32
3
u −
11
3
(ii) Obstruction class = −1
(iii) Cusp Shapes =
17
12
u
5
−
85
12
u
4
+ 21u
3
−
85
4
u
2
+
25
6
u −
19
3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 4u
5
+ 24u
4
+ 11u
3
+ 42u
2
− 11u + 1)
2
c
2
, c
4
(u
6
− 2u
5
+ 3u
3
+ 6u
2
− u + 1)
2
c
3
, c
7
(u
6
− 7u
5
+ 26u
4
− 51u
3
+ 52u
2
− 28u + 8)
2
c
5
, c
8
u
12
+ 2u
11
+ ··· + 15u + 9
c
6
, c
9
u
12
− 6u
11
+ ··· − 1017u + 603
c
10
, c
12
u
12
− u
11
+ ··· − 942u + 423
c
11
(u
6
− u
5
+ 5u
3
− 4u + 8)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ 32y
5
+ 572y
4
+ 1985y
3
+ 2054y
2
− 37y + 1)
2
c
2
, c
4
(y
6
− 4y
5
+ 24y
4
− 11y
3
+ 42y
2
+ 11y + 1)
2
c
3
, c
7
(y
6
+ 3y
5
+ 66y
4
− 273y
3
+ 264y
2
+ 48y + 64)
2
c
5
, c
8
y
12
+ 16y
10
+ ··· + 189y + 81
c
6
, c
9
y
12
+ 16y
11
+ ··· + 402057y + 363609
c
10
, c
12
y
12
+ 29y
11
+ ··· − 1840806y + 178929
c
11
(y
6
− y
5
+ 10y
4
− 17y
3
+ 40y
2
− 16y + 64)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375593 + 0.540780I
a = 0.486099 − 0.455368I
b = −0.834769 + 0.886986I
0.10873 + 3.16633I −6.33370 − 4.19720I
u = 0.375593 + 0.540780I
a = 0.92528 + 1.97320I
b = 0.226390 + 0.446346I
0.10873 + 3.16633I −6.33370 − 4.19720I
u = 0.375593 − 0.540780I
a = 0.486099 + 0.455368I
b = −0.834769 − 0.886986I
0.10873 − 3.16633I −6.33370 + 4.19720I
u = 0.375593 − 0.540780I
a = 0.92528 − 1.97320I
b = 0.226390 − 0.446346I
0.10873 − 3.16633I −6.33370 + 4.19720I
u = 1.391620 + 0.251770I
a = −0.698843 − 0.090535I
b = −2.07845 − 0.66940I
−0.10873 − 3.16633I −5.66630 + 4.19720I
u = 1.391620 + 0.251770I
a = −0.09615 − 1.82357I
b = 0.112878 − 1.032920I
−0.10873 − 3.16633I −5.66630 + 4.19720I
u = 1.391620 − 0.251770I
a = −0.698843 + 0.090535I
b = −2.07845 + 0.66940I
−0.10873 + 3.16633I −5.66630 − 4.19720I
u = 1.391620 − 0.251770I
a = −0.09615 + 1.82357I
b = 0.112878 + 1.032920I
−0.10873 + 3.16633I −5.66630 − 4.19720I
u = 1.73279 + 2.49487I
a = 1.070440 − 0.329156I
b = 2.03504 + 0.00711I
−19.7392 − 6.3327I −6.00000 + 2.82663I
u = 1.73279 + 2.49487I
a = −1.186840 − 0.318891I
b = −1.96109 − 0.25888I
−19.7392 − 6.3327I −6.00000 + 2.82663I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73279 − 2.49487I
a = 1.070440 + 0.329156I
b = 2.03504 − 0.00711I
19.7392 + 6.3327I −6.00000 − 2.82663I
u = 1.73279 − 2.49487I
a = −1.186840 + 0.318891I
b = −1.96109 + 0.25888I
19.7392 + 6.3327I −6.00000 − 2.82663I
15
IV. I
u
4
= h2u
2
b + b
2
− bu + 4u
2
+ 4b − 2u + 7, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
−u
2
+ u − 2
b
a
11
=
−u
2
+ u − 2
b − u
a
7
=
u
u
2
− u + 1
a
6
=
u
2
+ b + 2
2u
2
b + 3u
2
+ b − u + 5
a
9
=
u
2
b − 1
−bu + 2b + 1
a
12
=
−u
2
+ u − 2
b − u
a
1
=
0
−u
a
5
=
u
u
2
− u + 1
a
2
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 7u − 16
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
8
c
9
u
6
− 3u
5
+ 5u
4
− 5u
3
+ 5u
2
− 3u + 1
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
, c
12
(u + 1)
6
c
11
u
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
8
c
9
y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1
c
10
, c
12
(y −1)
6
c
11
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = −0.715080 − 0.241870I
1.37919 − 2.82812I −1.19557 + 4.65175I
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = 0.254878 + 0.424452I
1.37919 − 2.82812I −1.19557 + 4.65175I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = −0.715080 + 0.241870I
1.37919 + 2.82812I −1.19557 − 4.65175I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = 0.254878 − 0.424452I
1.37919 + 2.82812I −1.19557 − 4.65175I
u = 0.569840
a = −1.75488
b = −2.03980 + 1.73159I
−2.75839 −14.6090
u = 0.569840
a = −1.75488
b = −2.03980 − 1.73159I
−2.75839 −14.6090
19
V. I
v
1
= ha, −v
3
− 7v
2
+ 4b − 12v − 1, v
4
+ 7v
3
+ 16v
2
+ 13v + 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
10
=
0
1
4
v
3
+
7
4
v
2
+ 3v +
1
4
a
11
=
v
3
+ 3v
2
+ v
1
4
v
3
+
7
4
v
2
+ 3v +
1
4
a
7
=
v
0
a
6
=
2v
3
+ 9v
2
+ 11v + 4
−
3
4
v
3
−
17
4
v
2
− 7v −
11
4
a
9
=
−v
3
− 3v
2
− v
1
4
v
3
+
3
4
v
2
−
3
4
a
12
=
−v
3
4
v
3
+
17
4
v
2
+ 7v +
7
4
a
1
=
−v
−1
a
5
=
v
1
a
2
=
−v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
51
16
v
3
−
217
16
v
2
−
83
4
v −
311
16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
u
4
+ u
2
− u + 1
c
8
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
, c
10
, c
12
u
4
+ u
2
+ u + 1
c
11
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
6
, c
9
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
11
y
4
− y
3
+ 2y
2
+ 7y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.600768 + 0.325640I
a = 0
b = −1.112690 + 0.371716I
−2.62503 + 1.39709I −10.34643 − 2.46427I
v = −0.600768 − 0.325640I
a = 0
b = −1.112690 − 0.371716I
−2.62503 − 1.39709I −10.34643 + 2.46427I
v = −2.89923 + 0.40053I
a = 0
b = 0.237691 − 0.353773I
0.98010 + 7.64338I 2.12768 − 8.80169I
v = −2.89923 − 0.40053I
a = 0
b = 0.237691 + 0.353773I
0.98010 − 7.64338I 2.12768 + 8.80169I
23
VI. I
v
2
= ha, −v
2
b + b
2
+ 2bv − v
2
+ b + 2v + 1, v
3
− 3v
2
+ 2v − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
10
=
0
b
a
11
=
−v
2
b
b
a
7
=
v
0
a
6
=
−v
2
b + bv − v
2
+ 2v
−v
2
b + 3bv − v
2
− b + 3v − 1
a
9
=
v
2
b − bv + b + v
−bv + v
2
+ b − 3v + 1
a
12
=
−bv + v
2
− 2v + 1
−v
2
+ 3v − 2
a
1
=
−bv + v
2
− 2v + 1
−1
a
5
=
bv − v
2
+ 2v − 1
1
a
2
=
−bv + v
2
− 2v + 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7v
2
− 13v − 5
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
, c
10
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
11
(u
3
− u
2
+ 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
y
6
c
5
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
6
, c
9
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
11
(y
3
− y
2
+ 2y − 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.337641 + 0.562280I
a = 0
b = −0.960138 + 0.693124I
−1.37919 + 2.82812I −10.80443 − 4.65175I
v = 0.337641 + 0.562280I
a = 0
b = −0.91730 − 1.43799I
−1.37919 + 2.82812I −10.80443 − 4.65175I
v = 0.337641 − 0.562280I
a = 0
b = −0.960138 − 0.693124I
−1.37919 − 2.82812I −10.80443 + 4.65175I
v = 0.337641 − 0.562280I
a = 0
b = −0.91730 + 1.43799I
−1.37919 − 2.82812I −10.80443 + 4.65175I
v = 2.32472
a = 0
b = −0.122561 + 0.479689I
2.75839 2.60890
v = 2.32472
a = 0
b = −0.122561 − 0.479689I
2.75839 2.60890
27
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
3
− u
2
+ 2u − 1)
2
· (u
6
+ 4u
5
+ 24u
4
+ 11u
3
+ 42u
2
− 11u + 1)
2
· (u
9
− 10u
8
+ 29u
7
− 39u
6
+ 26u
5
− 15u
4
+ 19u
3
− 8u
2
− 3u − 1)
· (u
14
+ 54u
13
+ ··· − 7647u + 256)
c
2
(u − 1)
10
(u
3
+ u
2
− 1)
2
(u
6
− 2u
5
+ 3u
3
+ 6u
2
− u + 1)
2
· (u
9
+ 4u
8
+ 3u
7
− 5u
6
− 10u
5
− 5u
4
+ 3u
3
+ 6u
2
+ 3u + 1)
· (u
14
− 16u
13
+ ··· + 31u − 16)
c
3
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
6
− 7u
5
+ 26u
4
− 51u
3
+ 52u
2
− 28u + 8)
2
· (u
9
+ 5u
8
+ 8u
7
+ 13u
6
+ 10u
5
+ 11u
4
+ 5u
3
+ 6u
2
+ u + 1)
· (u
14
+ 21u
13
+ ··· + 544u + 256)
c
4
(u + 1)
10
(u
3
− u
2
+ 1)
2
(u
6
− 2u
5
+ 3u
3
+ 6u
2
− u + 1)
2
· (u
9
− 4u
8
+ 3u
7
+ 5u
6
− 10u
5
+ 5u
4
+ 3u
3
− 6u
2
+ 3u − 1)
· (u
14
− 16u
13
+ ··· + 31u − 16)
c
5
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
− 3u
5
+ 5u
4
− 5u
3
+ 5u
2
− 3u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
9
− 3u
8
+ 5u
7
− 4u
6
+ 2u
5
− 2u
4
+ 4u
3
− 3u
2
+ 1)
· (u
12
+ 2u
11
+ ··· + 15u + 9)(u
14
+ 2u
13
+ ··· + 4u + 1)
c
6
(u
4
+ u
2
− u + 1)(u
6
− 3u
5
+ 5u
4
− 5u
3
+ 5u
2
− 3u + 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
9
− 3u
7
+ 4u
6
− 2u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1)
· (u
12
− 6u
11
+ ··· − 1017u + 603)(u
14
− 11u
13
+ ··· + 9u − 9)
c
7
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
6
− 7u
5
+ 26u
4
− 51u
3
+ 52u
2
− 28u + 8)
2
· (u
9
− 5u
8
+ 8u
7
− 13u
6
+ 10u
5
− 11u
4
+ 5u
3
− 6u
2
+ u − 1)
· (u
14
+ 21u
13
+ ··· + 544u + 256)
c
8
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
6
− 3u
5
+ 5u
4
− 5u
3
+ 5u
2
− 3u + 1)
· (u
9
− 3u
8
+ 5u
7
− 4u
6
+ 2u
5
− 2u
4
+ 4u
3
− 3u
2
+ 1)
· (u
12
+ 2u
11
+ ··· + 15u + 9)(u
14
+ 2u
13
+ ··· + 4u + 1)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− 3u
5
+ 5u
4
− 5u
3
+ 5u
2
− 3u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
9
− 3u
7
+ 4u
6
− 2u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1)
· (u
12
− 6u
11
+ ··· − 1017u + 603)(u
14
− 11u
13
+ ··· + 9u − 9)
c
10
, c
12
(u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
9
+ 6u
8
+ 5u
7
+ 12u
6
+ 6u
5
+ 10u
4
+ 5u
2
− u + 1)
· (u
12
− u
11
+ ··· − 942u + 423)(u
14
+ 27u
13
+ ··· + 157u − 1)
c
11
u
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)(u
6
− u
5
+ 5u
3
− 4u + 8)
2
· (u
9
− 3u
8
− 7u
7
+ 61u
6
− 171u
5
+ 279u
4
− 297u
3
+ 212u
2
− 97u + 23)
· (u
14
+ 22u
13
+ ··· + 88u + 4)
28
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
3
+ 3y
2
+ 2y − 1)
2
· (y
6
+ 32y
5
+ 572y
4
+ 1985y
3
+ 2054y
2
− 37y + 1)
2
· (y
9
− 42y
8
+ ··· − 7y − 1)(y
14
− 910y
13
+ ··· − 4.04127 × 10
7
y + 65536)
c
2
, c
4
(y − 1)
10
(y
3
− y
2
+ 2y − 1)
2
· (y
6
− 4y
5
+ 24y
4
− 11y
3
+ 42y
2
+ 11y + 1)
2
· (y
9
− 10y
8
+ 29y
7
− 39y
6
+ 26y
5
− 15y
4
+ 19y
3
− 8y
2
− 3y − 1)
· (y
14
− 54y
13
+ ··· + 7647y + 256)
c
3
, c
7
y
10
(y
3
+ 3y
2
+ 2y − 1)
2
· (y
6
+ 3y
5
+ 66y
4
− 273y
3
+ 264y
2
+ 48y + 64)
2
· (y
9
− 9y
8
− 46y
7
− 109y
6
− 164y
5
− 171y
4
− 113y
3
− 48y
2
− 11y − 1)
· (y
14
− 177y
13
+ ··· − 226304y + 65536)
c
5
, c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1)
· (y
9
+ y
8
+ 5y
7
+ 10y
5
− 6y
4
+ 12y
3
− 5y
2
+ 6y − 1)
· (y
12
+ 16y
10
+ ··· + 189y + 81)(y
14
− 2y
13
+ ··· − 6y + 1)
c
6
, c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
9
− 6y
8
+ 5y
7
− 12y
6
+ 6y
5
− 10y
4
− 5y
2
− y − 1)
· (y
12
+ 16y
11
+ ··· + 402057y + 363609)
· (y
14
− 61y
13
+ ··· − 927y + 81)
c
10
, c
12
(y − 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
9
− 26y
8
+ ··· − 9y − 1)(y
12
+ 29y
11
+ ··· − 1840806y + 178929)
· (y
14
− 413y
13
+ ··· − 22155y + 1)
c
11
y
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
6
− y
5
+ 10y
4
− 17y
3
+ 40y
2
− 16y + 64)
2
· (y
9
− 23y
8
+ ··· − 343y − 529)(y
14
− 64y
13
+ ··· − 2456y + 16)
29
